Optimal Reconfigurable Intelligent Surface Placement in Millimeter-Wave Communications

Abstract

In this work, we examine the use of reconfigurable intelligent surfaces (RISs) to create alternative paths from a transmitter to a receiver in millimeter-wave (mmWave) networks, when the direct link is blocked. In this direction, we evaluate the end-to-end signal-to-noise ratio (SNR) expression of the transmitter-RIS-receiver links that take into account the transmitter-RIS and RIS receiver distances and enable us to acquire important insights regarding the RIS position that maximizes it. Finally, the insights are corroborated by numerical results.

Full text

Optimal Reconfigurable Intelligent Surface
Placement in Millimeter-Wave Communications
Konstantinos Ntontin∗, Dimitrios Selimis∗, Alexandros-Apostolos A. Boulogeorgos†, Antonis Alexandridis∗,
Aris Tsolis∗, Vasileios Vlachodimitropoulos∗, and Fotis Lazarakis∗
∗Institute of Informatics and Telecommunications, National Centre for Scientific Research "Demokritos", Greece,
e-mail: {konstantinos.ntontin, dselimis, aalex, atsolis, vvlachod, flaz }@iit.demokritos.gr
†Department of Digital Systems, University of Piraeus, Greece, e-mail: al.boulogeorgos@ieee.org
Abstract—In this work, we examine the use of recon-
figurable intelligent surfaces (RISs) to create alternative
paths from a transmitter to a receiver in millimeter-wave
(mmWave) networks, when the direct link is blocked. In
this direction, we evaluate the end-to-end signal-to-noise
ratio (SNR) expression of the transmitter-RIS-receiver
links that take into account the transmitter-RIS and RIS-
receiver distances and enables us to acquire important
insights regarding the RIS position that maximizes it.
Finally, the insights are corroborated by numerical results.
I. INTRODUCTION
Increasing data-rate demands have led current mobile-access
networks relying on sub-6 GHz bands reach their limits in
terms of available bandwidth. This bottleneck created the need
to examine above-6 GHz bands for mobile-access networks.
Currently, bands in the lower-end mmWave spectrum are used
for point-to-point and point-to-multipoint line-of-sight (LOS)
wireless backhaul/fronthaul and fixed-wireless access net-
works [1]. Such deployments span the 30-100 GHz operational
frequency range. However, the expected migration of future
mobile-access networks to the 30-100 GHz band pushes the
corresponding wireless backhaul/fronthaul links towards the
beyond-100 GHz bands. Due to this, backhauling/fronthauling
transceiver equipment vendors have performed LOS trials in
the D band (130-174.8 GHz), which showcase the potential of
using it in such deployments [2]. Apart from LOS, street-level
deployments in dense urban scenarios necessitate devising
non-LOS (NLOS) solutions since LOS links may not always
be ensured. However, despite the fact that according to mea-
surements [3], [4] NLOS communication through scattering
and reflection from objects in the radio path is feasible in the
30-100 GHz range, the higher propagation loss of beyond-100
GHz bands is likely to put such communication into question.
The conventional approach of counteracting NLOS links
is by providing alternative LOS routes through relay nodes
[5]. Although this is a well-established method to increase the
coverage when the signal quality of the direct links is low, it is
argued that it cannot constitute a viable approach for massive
deployment, especially for mmWave networks. This is due to
the increased power consumption of the active radio-frequency
(RF) components in high frequencies that relays need to
be equipped with [6]. Apart from relaying, communication
through passive non-reconfigurable specular reflectors, such as
dielectric mirrors, has been proposed as another alternative.
Such a method for coverage enhancement has the potential
to be notably more cost efficient compared with relaying
and has been documented at both mmWave and beyond-100
GHz bands [6], [7]. Due to the highly dynamic nature of
blockage at high frequencies, it would be desirable that such
reflectors can change the angle of departure of the waves
based on changing blockage conditions so that they direct the
beams towards different routes. However, passive reflectors
are incapable of supporting the aforementioned functionality
since the conventional Snell’s law applies. Based on the above,
an intriguing question that arises is: Would it be possible to
deploy reconfigurable reflectors that can arbitrarily steer the
impinging beam based on dynamic blockage conditions? The
answer is affirmative by considering the RIS paradigm.
RISs are two-dimensional structures of dielectric material,
in which tunable reflecting elements are embedded [8–11].
They constitute a substantially different technology than re-
laying, owing to their independence from bulky and power-
hungry analog electronic components, such as power ampli-
fiers and low-noise amplifiers. Additionally, their operation,
in contrast with relaying, does not require dividers and com-
biners, which can incur high insertion losses. By individually
tuning the phase response of each individual RIS element, the
reflected signals can constructively aggregate at a particular
focal point, such as the receiver. Such a tuning can be
enabled by electronic phase-switching components, such as
PIN diodes, RF-microelectromechanical systems, and varactor
diodes, that are introduced between adjacent elements [12].
Hence, RISs offer an alternative-to-relaying method for large-
scale beamforming without the incorporation of high power
consuming electronics and insertion losses involved by the ad-
ditional circuitry. In practice, the RIS element phase shift can
be controlled by a central controller through programmable
software [12].
Motivation and contribution: Previous works on RISs
mostly consider NLOS channels with respect to the
transmitter-RIS and RIS-receiver links, which make them
rather suitable for sub-6 GHz omnidirectional communica-
tions. Likewise, the employed models assume that the whole

RIS surface is illuminated regardless of the transmitter-RIS
distance. However, due to the fact that RISs in future networks
are expected to cover large portions of sizeable structures, such
as buildings, only a portion of the total RIS area would be illu-
minated, which depends on the aforementioned distance. Such
a reasoning necessitates the derivation of a novel expression
of the end-to-end SNR that incorporates such a dependence.
Based on the above, in this work we derive the corresponding
SNR expression in a mmWave RIS-aided link and use it to
extract important insights regarding the RIS placement that
maximizes the resulting expression. Furthermore, the findings
are validated by means of numerical simulations.
The rest of this work is structured as follows: In Section
II, we present the scenario under consideration together with
its main assumptions. In Section III, we derive the resulting
end-to-end SNR expression, which we use to extract important
insights regarding the optimal positioning of the RIS. Numeri-
cal results that validate the theoretical findings are provided in
Section IV, whereas Section V concludes this work and gives
ideas for future work.
II. SYSTEM MODEL
In this section, we first present the scenario under consid-
eration and, subsequently, the main assumptions.
A. Scenario
We consider a communication between a street-level trans-
mitter and receiver, as depicted in Fig. 1, in a mmWave highly
directional link1. The transmitter and receiver are equipped
with large, with respect to the wavelength, antennas that enable
communication through highly directive beams. Furthermore,
we assume that due to a fixed or moving obstacle the direct
communication is not possible, which can be the case for
highly directive beams and large carrier frequencies. In such
a case, the transmitter redirects the beam to an RIS mounted
on some fixed structure, such a tall building. The RIS acts a
beamformer by adjusting the phase response of the elements
so that the beam is directed towards the receiver. Moreover, we
consider that both the transmitter-RIS and RIS-receiver links
are subject to LOS conditions and that the RIS is located in
the far field of both the transmit and receive antennas.
B. Main Assumptions
We consider that the size of the RISs in the network is
sufficiently large so that the area illuminated by the main
lobe of a transmitted beam is smaller than RIS area. Such
an assumption is justified by the fact that it is expected that
RISs in future networks are going to cover large portions
of the building facades. In addition, their size needs to be
sufficiently large so that they can simultaneously accommodate
the transmissions of different transmitters. By considering
that under pencil-beam transmissions almost all the transmit
energy is located in the half-power beamwidth area (HPBW)
of the main lobe [6] and that the main-lobe shape is conical,
1As pointed out in Section I, such a link could be a fixed point-to-point
link of an upcoming beyond-100 GHz backhaul/fronthaul network.
Obstacle
Transmitter Receiver
RIS
Fig. 1: Communication through an RIS.
RIS
Obstacle
rRIS
φΤx
rTx,RIS
Transmitter
Receiver
Fig. 2: Illuminated RIS area.
approximately a circular area of the RIS is illuminated by the
transmission2with radius rRIS , given by
rRIS =tan φT x
2rT x,RIS ,(1)
where φT x is the HPBW of the transmitted beam and rT x,RIS
is the distance between the centers of the transmitter and
the RIS, as depicted in Fig. 2. By assuming, without loss of
generality, a parabolic reflector as a transmit antenna with a
diameter DT x, it approximately holds that [13]
φT x ≈1.22 λ
DT x
.(2)
Consequently, the illuminated RIS area, which is denoted
by SRIS , can be approximated by
SRIS ≈πr2
RIS .(3)
Finally, we assume that the received signal is subject to
additive white Gaussian noise. Its power level in dBm for a
bandwidth W, denoted by N0, is equal to
N0=−174 + 10 log10 (W) + FdB,(4)
2The actual shape of the illuminated RIS area depends on the angle of
incidence of the impinging wave on the RIS. It is a circle for angle of incidence
equal to 0◦and an ellipse for angles greater than 0◦, according to the theory
of conical cross sections. However, in this work our primary focus is on the
resulting SNR expression and the optimal RIS positioning based on it, where
the latter does not depend on the shape of the RIS illuminated area. Due to
this, we consider the circular footprint model in order to simplify the final
SNR expression.

where FdB is the noise figure in dB and Wis the transmission
bandwidth [14].
III. SNR AND OPTIMAL RIS PLACE ME NT
In this section, we firstly compute the received SNR of the
considered RIS-aided communication. Subsequently, based on
the expression, we comment on the optimal RIS placement.
Proposition 1: By assuming that all the RIS elements have
the same amplitude reflection coefficient, denoted by Γ, the
maximum received power, which we denote by Prmax , can be
approximated as
Prmax ≈
PT xtan4φT x
2Γ2GT xGRx cos θ(arr )
0cos θ(dep)
0
16
×rT x,RIS
rRIS,Rx 2
,(5)
where PT x is the transmit power. GT x is the gain of the
transmit antenna, GRx is the gain of the receive antenna, θ(arr)
0
is the incidence angle on the RIS, θ(dep)
0is the departure angle
from the RIS, and rRIS,Rx is the distance between the centers
of the RIS and the receiver.
Proof : See Appendix A.
Assuming parabolic reflector antennas at the transmitter and
the receiver with diameters DTx and DRx, respectively, it
holds that
Gm=πDm
λ2
em, m ={T x, Rx},(6)
where eT x and eRx are the aperture efficiencies of the transmit
and receive parabolic reflectors, respectively.
As a result, the equivalent end-to-end SNR at the receiver
can be approximated as
SN R ≈
Ptxtan4φT x
2Γ2GT xGRx cos θ(arr )
0cos θ(dep)
0
16N0
×rT x,RIS
rRIS,Rx 2
.(7)
Remark 1: Based on (7), an important question that arrises
is whether a transmitter should focus its beam towards an
RIS that is closer to the transmitter or closer to the receiver.
From (7), we observe that the SNR expression depends on the
transmitter-RIS and RIS-receiver distances through the ratio
rT x,RIS
rRIS,Rx and the terms cos θ(arr)
0and cos θ(dep)
0. The latter
holds since the angles of incidence θ(arr)
0and departure θ(dep)
0
depend on rT x,RIS and rRIS,Rx. In particular, for an RIS
with axis parallel to the ground (without loss of generality)
the closer the RIS to the transmitter is, the smaller the angle
of arrival and the larger the angle of departure are, with
respect to the RIS normal. The opposite holds the closer
the RIS to the receiver is. Hence, targeting an RIS that is
closer to the transmitter or to the receiver would roughly have
the same effect on the value of the term cos θ(arr)
0cos θ(dep)
0
that is included in (7). As a result, the equivalent end-to-end
SNR expression is expected to be mainly determined by the
value of the ratio rT x,RIS
rRIS,Rx . The particular ratio reveals that the
hTx hRx
hRIS
rTX,Rx,hor
φTX
rTx,Rx
rTx,RIS rRIS,Rx
rTX,RIS,hor
θ0(dep)
θ0(arr)
Transmitter Receiver
Fig. 3: 2D simulation setup.
transmitter should target an RIS that is closer to the receiver
than the transmitter so that the equivalent end-to-end SNR is
maximized.
IV. NUMERICAL RES ULTS
The aim of this section is to validate Remark 1 regarding
the optimal RIS positioning that maximizes the end-to-end
equivalent SNR by means of simulations. Towards this, we
consider the 2D point-to-point simulation setup that is depicted
in Fig. 3, in which the axis of the RIS is parallel to the ground.
According to the considered geometry, it holds that
rT x,RIS =qr2
T x,RIS hor + (hRIS −hT x )2,
rRIS,Rx =q(rT x,Rx,hor −rT x,RIS hor )2+ (hRIS −hRx )2,
θ(arr)
0=tan−1rT x,RIS,hor
hRIS −hT x ,
θ(dep)
0=tan−1|rT x,Rx,hor −rT x,RI Shor |
hRIS −hRx .
(8)
TABLE I: Parameter values used in the simulation.
f140 GHz
PT x 1 W
W2 GHz
FdB 10 dB
rT x,Rx,hor 40 m
hRIS 15 m
hT x,hRx 3 m
DT x,DRx 10 cm
eT x,eRx 1
Γ0.9
In Table I, we present the considered values for the involved
parameters in the simulation3.
3The value hRIS = 15 m can be a typical value for an RIS that is located
in the top of a 5-floor building facade by considering that the height of each
floor is around 3 m. In addition, the values hT x =hRx = 3 m can typically
correspond to transmitter and receiver nodes that are mounted on lampposts.

0 10 20 30 40 50 60
90
95
100
105
110
115
120
rTx,RIS,hor [m]
SNR [dB]
Fig. 4: SNR vs. the horizontal transmitter-RIS distance.
0 10 20 30 40 50 60
0
0.5
1
1.5
2
2.5
rTx,RIS,hor [m]
SRIS [m2]
Fig. 5: RIS area vs. the horizontal transmitter-RIS distance.
Regarding the optimal direction of towards a large RIS
surface that the transmitter should focus its beam on or,
from another perspective, the optimal placement of an RIS,
in Fig. 4 we illustrate the SNR as a function of the horizontal
transmitter-RIS distance, where the SNR is computed accord-
ing to (7). As we observe from Fig. 4, for SNR maximization
the transmitter should focus its beam on a point on the RIS
area that is very close to the receiver. Hence, Remark 1 is
validated. Moreover, we observe that substantial SNR gains,
in particular more than 20 dB, are achieved by the optimal
beam focusing compared with, for instance, the focusing on
the point on the RIS area that is vertically above the transmitter
(rT x,RIS,hor = 0). In addition, in Fig. 5 we illustrate SRIS as a
function of the horizontal transmitter-RIS distance. We observe
that at the distance for which the maximum SNR is obtained
the corresponding illuminated RIS area is approximately equal
to 1 m2. Consequently, this showcases the feasibility of such
a deployment since RIS surfaces with areas much larger than
1m2can be installed onto large building facades. Finally, we
note that in the simulated scenario the illuminated RIS area
is located in the far field of both the transmit and receive
antennas, as it is required in our model. This is due to the
fact that the Fraunhofer distance is equal to 2D2
m/λ = 10 m,
m={T x, Rx}, for both the transmit and receive antennas
and the minimum distance between the possible RIS location
and the aforementioned antennas is equal to 12 m.
V. CONCLUSIONS
We have conducted this work in order to determine the
optimal RIS placement with respect to the transmitter and
receiver antenna positioning. Towards this, we have considered
a realistic mmWave scenario in which the RIS area that is
illuminated by the transmitted very directional beam is smaller
than the total RIS area, which is expected in forthcoming RIS
deployments. Based on this model, we have quantified the
equivalent end-to-end SNR, which reveals that the RIS should
be optimally placed closer to the receiver than the transmitter
so that the SNR is maximized. Such an analytical outcome
was validated by means of simulations, which showed that
substantial gains are expected by the optimal deployment.
Future work will focus on the comparison of an RIS- and a
relay-aided point-to-point scenario in terms of coverage prob-
ability and rate, where the optimal deployments are considered
for both cases.
ACKNOWLEDGEMENTS
This work has reveived funding from the H2020 ARIADNE
project (Grant Agreement no. 871464).
APPENDIX
A. Proof of Proposition 1
The incident wave on the RIS nth element is given by
Einc,n =Eince−j2π
λrT x,RISnˆ
ax,(9)
where rT x,RISnis the distance between the transmitter and
the nth element of the illuminated RIS area. Considering that
the spatial power density of the incident electric wave on the
nth element of the RIS is approximately4equal to PT xGT x
4πr2
T x,RIS
,
it holds that E2
inc
2η=PT xGT x
4πr2
T x,RIS
,(10)
where ηis the free-space impedance. The captured power by
the nth element, denoted by Pcap,n, of the RIS is given by
Pcap,n =E2
inc
2ηAeff ,n =λ
4π2PT xGT x GRIS,n θ(arr)
0
r2
T x,RIS
,(11)
where Aeff,n =λ2
4πGRIS,n θ(arr)
0is the effective aperture
of the nth RIS element with GRIS,n θ(arr)
0being its gain.
Based on the passive reflector theory, it holds that [13]
GRIS,n θ(arr )
0=4π
λ2dxdycos θ(arr)
0,(12)
where dxand dyare the x and y-axis dimensions of each RIS
element, respectively. The term dxdycos θ(arr)
0represents
the projected surface on the RIS seen by the transmitter.
4Considering that rT x,RISn≈rT x,RI S due to the far-field operation.

The spatial power density at the receiver antenna after re-
flection from the nth element, which is denoted by Prspatial,n ,
is given by
Prspatial,n =Pcap,n
Γ2GRIS,n θ(dep)
01
4πr2
RIS,Rx
=λ2
(4π)3
PT xΓ2GT x GRIS,n θ(arr)
0GRIS,n θ(dep)
0
r2
T x,RIS r2
RIS,Rx
,
(13)
where, as in the transmission towards the RIS case, it is
assumed that due to the far-field positioning of the receiver
antenna with respect to the RIS it holds that rRISn,Rx ≈
rRIS,Rx , where rRISn,Rx is the distance from the center of
the nth RIS element to the center of the receiver antenna.
In addition, GRIS,n θ(dep)
0is the gain of the nth RIS
element involved in the radiation towards the receiver antenna.
Similarly to (12), it holds that
GRIS,n θ(dep)
0=4π
λ2dxdycos θ(dep)
0,(14)
where the term dxdycos θ(dep)
0represents the projected
surface on the RIS seen by the receiver.
Next, by assuming that the nth RIS element through its
corresponding switching element is adjusted so that the phase
of the departing beam related with the element is equal to
φRIS nand that mutual coupling among different elements
is negligible, the electric field of the impinging beam at the
receiver antenna, which we denote by Er,n, is given by
Er,n =Er,ne
−j φRISn+2π(rT x,RI Sn+rRISn,Rx )
λ!ˆ
ax,(15)
where
Er,n =q2ηPrspatial,n
=v
u
u
t2ηλ2
(4π)3
PT xΓ2GT x GRIS,n θ(arr)
0GRIS,n θ(dep)
0
r2
T x,RI S r2
RIS,Rx
.
(16)
The received power PrφRIS1, ..., φRISMxMyconsidering
the contribution from all the RIS elements is given by
P(RIS )
rφRIS1, ..., φRI SMxMy
=

PMxMy
n=1 Er,n


2
2η
λ2
4πGRx
=λ
4π4PT xΓ2GT x GRx
r2
T x,RIS r2
RIS,Rx
×





MxMy
X
n=1 rGRIS,n θ(arr)
0GRIS,n θ(dep)
0
×e
−j φRISn+2π(rT x,RI Sn+rRISn,Rx )
λ!





2
,(17)
where Mxand Myare the number of RIS elements in the x-
and y-axis, respectively.
From (17), it is evident that the received power is maximized
by setting
φRISn=−2π(rT x,RI Sn+rRISn,Rx )
λ.(18)
By taking into account that






MxMy
X
n=1 rGRIS,n θ(arr)
0GRIS,n θ(dep)
0





2
=GRIS θ(arr )
0GRIS θ(dep)
0,(19)
where
GRIS θ(s)
0=4π
λ2SRIS cos θ(s)
0, s ={arr, dep},(20)
and by using (1) and (3), the maximum value of
PrφRIS1, ..., φRI SMxMy,Prmax , is approximated by (5),
which concludes the proof.
REFERENCES
[1] “Mobile backhaul options: Spectrum analysis and recommendations,”
ABI Research, Tech. Rep., Sep. 2018.
[2] “Millimetre wave transmission (mwt); analysis of spectrum, license
schemes and network scenarios in the d-band,” ETSI, Tech. Rep., Aug.
2018.
[3] M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S.
Rappaport, and E. Erkip, “Millimeter Wave Channel Modeling and
Cellular Capacity Evaluation,” IEEE J. Sel. Areas Commun., vol. 32,
no. 6, pp. 1164–1179, June 2014.
[4] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G. N.
Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter Wave
Mobile Communications for 5G Cellular: It Will Work!” IEEE Access,
vol. 1, pp. 335–349, May 2013.
[5] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity
in wireless networks: Efficient protocols and outage behavior,” IEEE
Trans. Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.
[6] W. Khawaja, O. Ozdemir, Y. Yapici, F. Erden, and I. Guvenc, “Coverage
Enhancement for NLOS mmwave Links Using Passive Reflectors,” IEEE
Open Journal of the Communications Society, vol. 1, pp. 263–281, 2020.
[7] M. T. Barros, R. Mullins, and S. Balasubramaniam, “Integrated Terahertz
Communication With Reflectors for 5g Small-Cell Networks,” IEEE
Trans. Veh. Tech., vol. 66, no. 7, pp. 5647–5657, July 2017.
[8] Q. Wu and R. Zhang, “Beamforming optimization for intelligent reflect-
ing surface with discrete phase shifts,” in IEEE International Conference
on Acoustics, Speech and Signal Processing (ICASSP), 2019, pp. 7830–
7833.
[9] ——, “Towards smart and reconfigurable environment: Intelligent re-
flecting surface aided wireless network,” IEEE Commun. Mag., vol. 58,
no. 1, Nov. 2020.
[10] O. Özdogan, E. Björnson, and E. G. Larsson, “Intelligent reflecting
surfaces: Physics, propagation, and pathloss modeling,” IEEE Wirel.
Commun. Lett., vol. 9, no. 5, pp. 581–585, 2020.
[11] A. A. Boulogeorgos and A. Alexiou, “Performance Analysis of Recon-
figurable Intelligent Surface-Assisted Wireless Systems and Comparison
With Relaying,” IEEE Access, vol. 8, May 2020.
[12] E. Basar, M. D. Renzo, J. de Rosny, M.-S. Alouini, and R. Zhang,
“Wireless Communications Through Reconfigurable Intelligent Sur-
faces,” IEEE Access, vol. 7, pp. 116 753–116 773, Aug. 2019.
[13] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. John
Wiley, 2007.
[14] K. Ntontin, M. Di Renzo, and C. Verikoukis, “On the Feasibility of Full-
Duplex Relaying in Multiple-Antenna Cellular Networks,” IEEE Trans.
Commun., vol. 65, no. 5, pp. 2234–2249, May 2017.